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过度识别下的双重稳健识别与估计AI 解读

Consider two parametric models. At least one is correctly specified, but we do not know which. Both models include a common vector of parameters. An estimator for this common parameter vector is called Doubly Robust (DR) if it is consistent no matter which model is correct. We provide a general technique for constructing DR estimators (assuming the models are over identified). Our Over-identified Doubly Robust (ODR) technique is a simple extension of the Generalized Method…

线性工具变量模型中对识别强度稳健的非参数推断AI 解读

For a linear IV regression, we propose two new inference procedures on parameters of endogenous variables that are robust to any identification pattern, do not rely on a linear first-stage equation, and account for heteroskedasticity of unknown form. Building on Bierens (1982), we first propose an Integrated Conditional Moment (ICM) type statistic constructed by setting the parameters to the value under the null hypothesis. The ICM procedure tests at the same time the value…

贝叶斯多元保序回归中可信区间的覆盖率AI 解读

We consider the nonparametric multivariate isotonic regression problem, where the regression function is assumed to be nondecreasing with respect to each predictor. Our goal is to construct a Bayesian credible interval for the function value at a given interior point with assured limiting frequentist coverage. A natural prior on the regression function is given by a random step function with a suitable prior on increasing step-heights, but the resulting posterior…

异质幂律数据的极值推断AI 解读

We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which now estimates the extreme value index of the average distribution. Due to the heterogeneity, the asymptotic variance can be substantially smaller than that in the i.i.d. case. As a special case, we consider a heterogeneous scales model where the asymptotic variance can be calculated…

低秩模型的统计推断AI 解读

This paper studies inference in linear models with a high-dimensional parameter matrix that can be well approximated by a “spiked low-rank matrix.” A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero singular values that diverge to infinity. We show that this framework covers a broad class of models of latent variables, which can accommodate matrix completion problems, factor models, varying coefficient models and heterogeneous…

对抗损失下未知子流形上的分布估计极小极大速率AI 解读

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted a lot of attention. In machine learning, deep generative modelling approaches implicitly estimate distributions of complex objects by creating new samples from the underlying distribution, and have achieved great success in generating synthetic realistic-looking images and texts. A key step in these approaches is the extraction of latent features or representations…

跨尺度的扩散密度估计AI 解读

We consider a space structured population model generated by two-point clouds: a homogeneous Poisson process M with intensity n→∞ as a model for a parent generation together with a Cox point process N as offspring generation, with conditional intensity given by the convolution of M with a scaled dispersal density σ−1f(·/σ). Based on a realisation of M and N, we study the nonparametric estimation of f and the estimation of the physical scale parameter σ>0 simultaneously for…

非平稳时间序列的自回归近似、推断与应用AI 解读

Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time-series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range dependent nonstationary and nonlinear time series can be well approximated globally by a white-noise-driven autoregressive (AR) process of slowly diverging order. To our best knowledge, it is the first time such a structural approximation…

稠密正则图上 Ising 模型的统计推断AI 解读

In this paper, we derive the limit of experiments for one-parameter Ising models on dense regular graphs. In particular, we show that the limiting experiment is Gaussian in the “low temperature” regime, and non-Gaussian in the “critical” regime. We also derive the limiting distributions of the maximum likelihood and maximum pseudolikelihood estimators, and study limiting power for tests of hypothesis against contiguous alternatives. To the best of our knowledge, this is the…

利用基展开估计平稳 Gibbs 点过程的成对交互函数AI 解读

The class of Gibbs point processes (GPP) is a large class of spatial point processes able to model both clustered and repulsive point patterns. They are specified by their conditional intensity, which for a point pattern x and a location u, is roughly speaking the probability that an event occurs in an infinitesimal ball around u given the rest of the configuration is x. The most simple and natural class of models is the class of pairwise interaction point processes where…

残差子抽样的通用秩推断及其大型网络应用AI 解读

Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to rank inference via residual subsampling (RIRS) for testing and estimating rank in a wide family of models, including many popularly used network models such as the degree corrected mixed membership model as a special case. Our procedure constructs a test statistic via subsampling…

使用 ℓp 正则化统计量的 Model-X knockoffs 功效分析AI 解读

Variable selection properties of procedures utilizing penalized-likelihood estimates is a central topic in the study of high-dimensional linear regression problems. Existing literature emphasizes the quality of ranking of the variables by such procedures as reflected in the receiver operating characteristic curve or in prediction performance. Specifically, recent works have harnessed modern theory of approximate message-passing (AMP) to obtain, in a particular setting, exact…

通信约束下最优高维与非参数分布式检验AI 解读

We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central machine is limited to b bits. We investigate both the d- and infinite-dimensional signal detection problem under Gaussian white noise. We also derive distributed testing algorithms reaching the theoretical lower bounds. Our results show that distributed testing is subject to fundamentally different phenomena that are not observed in…

维数与样本量之比趋于无穷时样本协方差特征值统计量的渐近正态性及应用AI 解读

The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultrahigh-dimensional setting, that is, when the dimension to sample size ratio p/n→∞. Based on this CLT result, we extend the covariance matrix test problem to the new ultra-high-dimensional context, and apply it to test a matrix-valued white noise. Simulation experiments are conducted for the investigation of finite-sample properties of the…

局部渐近正态量子统计模型的估计效率AI 解读

We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators, such as quantum regular estimators and quantum minimax estimators, leading to a universal tight lower bound beyond the i.i.d. assumption. This formulation complements the theory of quantum contiguity developed in the previous paper [Fujiwara and Yamagata, Bernoulli 26 (2020)…

协变量自适应随机化下分位数处理效应的回归调整估计AI 解读

Datasets from field experiments with covariate-adaptive randomizations (CARs) usually contain extra covariates in addition to the strata indicators. We propose to incorporate these additional covariates via auxiliary regressions in the estimation and inference of unconditional quantile treatment effects (QTEs) under CARs. We establish the consistency and limit distribution of the regression-adjusted QTE estimator and prove that the use of multiplier bootstrap inference is…

Synthetic Learner：随时间变化的处理效应无模型推断AI 解读

Understanding the effect of a particular treatment or a policy pertains to many areas of interest, ranging from political economics, marketing to healthcare. In this paper, we develop a non-parametric algorithm for detecting the effects of treatment over time in the context of Synthetic Controls. The method builds on counterfactual predictions from many algorithms without necessarily assuming that the algorithms correctly capture the model. We introduce an inferential…

重复截面与连续处理下的非参数双重差分AI 解读

This paper studies the identification of causal effects of a continuous treatment using a new difference-in-difference strategy. Our approach allows for endogeneity of the treatment, and employs repeated cross-sections. It requires an exogenous change over time which affects the treatment in a heterogeneous way, stationarity of the distribution of unobservables and a rank invariance condition on the time trend. On the other hand, we do not impose any functional form…

二元治疗选择中的概率预测：聚焦个性化医疗AI 解读

This paper extends my research applying statistical decision theory to treatment choice with sample data, using maximum regret to evaluate the performance of statistical treatment rules. The specific new contribution is to study as-if optimization using estimates of illness probabilities in a class of medical decisions. Beyond its specifics, the paper sends a broad message. Statisticians and computer scientists have addressed conditional prediction for decision making in…

高维环境下基于 L2 提升的处理效应估计与推断AI 解读

Empirical researchers are increasingly faced with rich data sets containing many controls or instrumental variables, making it essential to choose an appropriate approach to variable selection. In this paper, we provide results for valid inference after post- or orthogonal L2-boosting is used for variable selection. We consider treatment effects after selecting among many control variables and instrumental variable models with potentially many instruments. To achieve this,…

竞争风险模型的部分识别：癌症死亡趋势应用AI 解读

Competing risks models for discretely measured durations are partially identifying due to the unknown dependence structure between risks and the discrete nature of the outcome. This article develops a highly tractable bounds approach for underlying distributions of latent durations by exploiting the discreteness. Bounds are obtained from a system of nonlinear (in)equalities. I devise a sequential solution method that requires much less computational burden than existing…

用于项目评估的前向选择面板数据方法AI 解读

Policy evaluation is central to economic data analysis, but economists mostly work with observational data in view of limited opportunities to carry out controlled experiments. In the potential outcome framework, the panel data approach (Hsiao et al., 2012) constructs the counterfactual by exploiting the correlation between cross-sectional units in panel data. The choice of cross-sectional control units, a key step in its implementation, is nevertheless unresolved in…

存在混杂类型时的处理效应识别AI 解读

In this paper, I consider identification of treatment effects when the treatment is endogenous. The use of instrumental variables is a popular solution to deal with endogeneity, but this may give misleading answers when the instrument is invalid. I show that when an (unobserved) instrument is invalid due to correlation with the first stage unobserved heterogeneity, a proxy for the instrument helps partially identify not only the local average treatment effect, but also the…

内生异方差下的处理效应估计AI 解读

This paper considers a treatment effect model in which individual treatment effect may be heterogeneous, even among observationally identical individuals. Specifically, by extending the classical instrumental-variables (IV) model with an endogenous binary treatment, the heteroskedasticity of the error disturbance is allowed to vary with the treatment variable so that the treatment generates both mean and variance effect on the outcome. In this endogenous heteroskedasticity…